PRACTICE COLLECTION / 39 PROBLEMS
Measurement & tools
Read instruments, resolve vectors and check dimensions. Each problem includes progressive hints, guided reasoning and a question to test the idea again. Problems marked “Free sample” are complete for everyone; membership opens the rest.
LEARN BEFORE YOU PRACTISE
Build the reasoning first.
Significant figures
What the digits in a measurement are allowed to claim
5 worked examples · 9 checks →Measurement uncertainty
What a reading tells you—and what it leaves unresolved
6 worked examples · 8 checks →Propagation of uncertainty
Follow the measurement model before choosing a formula
8 worked examples · 8 checks →Vectors and their components
Turn directions into equations without losing the geometry
4 worked examples · 7 checks →Units: keep the quantity, change the number
Use units as part of the calculation, including powers, rates and experimental scales.
4 worked examples · 5 checks →Read a vernier, understand the measurement
Derive the fine reading from two scales, correct the zero, and judge what the instrument can actually establish.
4 worked examples · 5 checks →Micrometer screw gauge
Turn rotation into length, then turn a reading into a defensible measurement.
6 worked examples · 6 checks →Make an experiment speak through a graph
Read slopes, intercepts and uncertainty as physical information rather than as a line-drawing exercise.
4 worked examples · 6 checks →Rates and accumulation: calculus for physics
Connect tangents, areas and initial conditions so that derivatives and integrals describe real changes.
7 worked examples · 7 checks →Exponential change, logarithms and controlled approximations
Recognise fractional change, solve for time and decide when a small-angle model is accurate enough.
7 worked examples · 7 checks →The cross product: perpendicular effects and direction
Build the geometry, signs and component method behind torque and magnetic force.
4 worked examples · 7 checks →Elastic response and measuring Young’s modulus
Separate material stiffness from specimen geometry, then infer a modulus from a controlled extension experiment.
6 worked examples · 8 checks →Standing waves, pipe modes and resonance measurements
Use boundary conditions to find nodes, harmonics and the information hidden in resonance spacings.
5 worked examples · 8 checks →Electrical instruments: meter ranges and bridge balances
Design a shunt or multiplier, quantify loading and infer an unknown resistance from a reproducible null.
7 worked examples · 6 checks →Magnifiers, telescopes, microscopes and focal measurements
Trace the intermediate image, define the viewing condition and connect optical models to a bench experiment.
9 worked examples · 8 checks →CONCEPTS IN THIS COLLECTION
PRACTISE AT YOUR PACE
Problems in this collection
39 problems · Showing 12
Measurement & tools
Correct the whole reading
The zero correction applies to the combined reading; it does not change the pitch or least count.
Read graphs & measurementsMeasurement & tools
Unpack a watt before converting area
What is the energy flux in SI units kg·s⁻³?
Apply a principleMeasurement & tools
Estimate first, then choose a power of ten
What is the nearest power of ten to its estimated molecule count, using distance on a logarithmic scale?
Compare casesMeasurement & tools
Keep the sign while removing the magnitude
What is the x component of the unit vector in its direction?
Apply a principleMeasurement & tools
Keep the last justified decimal
Choose the reporting rule for addition before rounding.
Apply a principleMeasurement & tools
Which measurement is relatively tighter?
Find the ratio of A’s relative bound to B’s relative bound.
Compare casesMeasurement & tools
A speedometer meets the SI system
Express its speed in m/s.
Apply a principleMeasurement & tools
A displacement with two components
The east and north components form perpendicular sides of a right triangle.
Apply a principleMeasurement & tools
A stack carries one zero offset
What is the inferred average sheet thickness?
Apply a principleMeasurement & tools
A diameter bound becomes an area bound
What is the approximate percentage bound on area?
Compare casesMeasurement & tools
Which component turns the arm?
Find the z component of torque about the pivot.
Apply a principleMeasurement & tools
Read stiffness from extension data
Find Young’s modulus.
Read graphs & measurements12 of 39 shown